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Gram - Schmıdt. or thogonalizan -wej) on Let P, = sın «x a

Gram - Schmıdt. or thogonalizan -wej) on Let P, = sın «x a

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter67: Analysis Of Trigonometric Functions
Section: Chapter Questions
Problem 51A
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Answer the following with full details and steps.
Gram -Schmidt. orthogonalizahio Let P, = sun «x a< x< b .. i i P = Cos aX. a <x 4. b SIn aax a <x<b. a Normaliza P, Pa, P3 e.g, P, with <P,IP> sin'ax dx C.g. 6 Find P, and P such that I .: © a Suggest a range for a and b that would systematize the math and make the calaulahans casier.
Transcribed Image Text:Gram -Schmidt. orthogonalizahio Let P, = sun «x a< x< b .. i i P = Cos aX. a <x 4. b SIn aax a <x<b. a Normaliza P, Pa, P3 e.g, P, with <P,IP> sin'ax dx C.g. 6 Find P, and P such that I .: © a Suggest a range for a and b that would systematize the math and make the calaulahans casier.
Expert Solution
Step 1

Gram Schmidt ortho normalization process:-

For vectors v1, v2, ......, vk the ortho normalized vectors are

uk=vk - ∑j=1k-1 uj.vkuj2.uj

 

Given that

p1=sinαx;   a<x<bp2=cosαx;   a<x<bp3=sin2αx;   a<x<b

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